An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is–

Options

A. `1:2`
B. `4:1`
C. `8:3`
D. `3:8`

Answer

A

Explanation

For 3rd harmonic / 2nd over tone of organ pipe open at ends.

`rArr n_(2) = (3v)/(2l_(2))`
For 1st overtone of orgain pipe open at one end

`rArr n_(1) = (3v)/(4l_(1))`
Given `n_(1) = n_(2) rArr (3v)/(2l_(1)) (3v)/(4l_(1))` or `(l_(1))/(l_(2)) = (1)/(2) `